Question

In: Finance

Suppose you hold a diversified portfolio consisting of a $6,406 invested equally in each of 5...

Suppose you hold a diversified portfolio consisting of a $6,406 invested equally

in each of 5 different common stocks.  The portfolio’s beta is 1.18.  Now

suppose you decided to sell one of your stocks that has a beta of 1 and to

use the proceeds to buy a replacement stock with a beta of 1.7.  What would

the portfolio’s new beta be?

1.12

1.02

0.92

1.22

1.32

Your portfolio consists of $80,406 invested in a stock that has a beta = 1.2,

$97,421 invested in a stock that has a beta = 0.8, and $99,775 invested in a

stock that has a beta = 1.5.  The risk-free rate is 1.8%.  Last year this portfolio had

a required return of 5.7%.  This year nothing has changed except that the market

risk premium has increased by 4.2%. What is the portfolio’s current required rate

of return?

10.6%

10.7%

10.9%

10.8%

11.0%

An investor is forming a portfolio by investing $86,534 in stock A that has a beta

of 2, and $23,817 in stock B that has a beta of 0.4. The market risk

premium is equal to 2.8% and Treasury bonds have a yield of 2.5%. What is the

required rate of return on the investor’s portfolio?

7.33%

7.53%

6.93%

7.13%

6.73%

Assume the risk-free rate is 2% and that the required return on the market is 3.9%.  

If a stock has a required rate of return of 10.5%, what is its beta?

5.09

4.47

3.57

4.87

3.07

Solutions

Expert Solution

1]

Beta of portfolio = weighted beta of each stock in the portfolio, with the weights being the proportion of the portfolio invested in each stock.

As it is an equally weighted portfolio, the weight of each stock = 1 / 5 = 0.2

New portfolio beta = old beta - (weighted beta of replaced stock) + (weighted beta of new stock)

New portfolio beta = 1.18 - (0.2 * 1) + (0.2 * 1.7)

New portfolio beta = 1.32

2]

First, we calculate the beta of the portfolio

Beta of portfolio = weighted beta of each stock in the portfolio, with the weights being the proportion of the portfolio invested in each stock.

weight of each stock = value of stock / value of portfolio

value of portfolio = total of value of stocks = $80,406 + $97,421 + $99,775 = $227,602

Beta of portfolio = (($80,406 / $227,602) * 1.2) + (($97,421 / $227,602) * 0.8) + (($99,775 / $227,602) * 1.5)

Beta of portfolio = 1.16745

Required return = risk free rate + (beta * market risk premium)

Substituting the values for last year into the above equation, we get :

5.87% = 1.8% + (1.16745 * market risk premium)

market risk premium = 3.4862%

New market risk premium this year = 3.4862% + 4.2% = 7.6862%

Required return = risk free rate + (beta * market risk premium)

Required return = 1.8% + (1.16745 * 7.6862%)

Required return = 10.8%

3]

First, we calculate the beta of the portfolio

Beta of portfolio = weighted beta of each stock in the portfolio, with the weights being the proportion of the portfolio invested in each stock.

weight of each stock = value of stock / value of portfolio

value of portfolio = total of value of stocks = $86,534 + $23,817 = $110,351

Beta of portfolio = (($86,534 / $110,351) * 2) + (($23,817 / $110,351) * 0.4)

Beta of portfolio = 1.16547

Required return = risk free rate + (beta * market risk premium)

Required return = 2.5% + (1.16547 * 2.8%)

Required return = 7.13%

4]

Required return = risk free rate + (beta * (required market return - risk free rate))

10.5% = 2% + (beta * (3.9% - 2%))

beta = (10.5% - 2%) / (3.9% - 2%)

beta = 4.47


Related Solutions

Suppose you hold a diversified portfolio consisting of a $10,000 invested equally in each of 10...
Suppose you hold a diversified portfolio consisting of a $10,000 invested equally in each of 10 different common stocks. The portfolio’s beta is 1.120. Now suppose you decided to sell two stocks with betas of 0.950 and 1.100, respectively and buy one stock with a beta of 1.750. What would the portfolio’s new beta be?
You hold a diversified portfolio consisting of a $10,000 investment in each of 20 different common...
You hold a diversified portfolio consisting of a $10,000 investment in each of 20 different common stocks (i.e., your total investment is $200,000). The portfolio beta is equal to 1.2 . You have decided to add another stock with a beta equal to 1.7 for $50,000. What will be the beta of the new portfolio? (Round to two digit decimal places)
Suppose you held a diversified portfolio consisting of a $7,500 investment in each of 20 different...
Suppose you held a diversified portfolio consisting of a $7,500 investment in each of 20 different common stocks. The portfolio's beta is 1.84. Now suppose you decided to sell one of the stocks in your portfolio with a beta of 1.0 for $7,500 and use the proceeds to buy another stock with a beta of 0.93. What would your portfolio's new beta be? Do not round intermediate calculations. Round your answer to two decimal places.
Suppose you held a diversified portfolio consisting of a $7,500 investment in each of 20 different...
Suppose you held a diversified portfolio consisting of a $7,500 investment in each of 20 different common stocks. The portfolio's beta is 0.75. Now suppose you decided to sell one of the stocks in your portfolio with a beta of 1.0 for $7,500 and use the proceeds to buy another stock with a beta of 1.60. What would your portfolio's new beta be? Do not round intermediate calculations. Round your answer to two decimal places.
Suppose you held a diversified portfolio consisting of a $7,500 investment in each of 20 different...
Suppose you held a diversified portfolio consisting of a $7,500 investment in each of 20 different common stocks. The portfolio's beta is 1.31. Now suppose you decided to sell one of the stocks in your portfolio with a beta of 1.0 for $7,500 and use the proceeds to buy another stock with a beta of 1.35. What would your portfolio's new beta be? Do not round intermediate calculations. Round your answer to two decimal places.
Suppose you hold a portfolio consisting of a $10,000 investment in each of 10 different common stocks.
Suppose you hold a portfolio consisting of a $10,000 investment in each of 10 different common stocks. The portfolio’s beta is 1.25. Now suppose you decided to make two changes to your portfolio as follows: a) sell stock X that has a beta of 1.0 and replace it with stock Y that has a beta od 1.5, andb) sell stock W that has a beta of 1.2 and replace it with stock Z that has a beta of 2.1. What would...
Suppose you hold a portfolio consisting of a $10,000 investment in each of 10 different common stocks.
Suppose you hold a portfolio consisting of a $10,000 investment in each of 10 different common stocks. The portfolio’s beta is 1.25. Now suppose you decided to make two changes to your portfolio as follows:a) sell stock X that has a beta of 1.0 and replace it with stock Y that has a beta od 1.5, andb) sell stock W that has a beta of 1.2 and replace it with stock Z that has a beta of 2.1. What would...
You hold a portfolio consisting of a $5,000 investment in each of 20 different stocks. The...
You hold a portfolio consisting of a $5,000 investment in each of 20 different stocks. The portfolio beta is equal to 1.12. You have decided to sell a coal mining stock (b = 1.00) at $5,000 net and use the proceeds to buy a like amount of a mineral rights company stock (b = 2.75). What is the new beta of the portfolio? Select the correct answer. a. 1.2075 b. 1.1895 c. 1.1955 d. 1.1835 e. 1.2015
Why, as an investor, should you try to hold a diversified portfolio?
Why, as an investor, should you try to hold a diversified portfolio?
Question # 03 Mr. Hatim hold a diversified portfolio consisting of Pakistan State Oil, OGDC, Mobilink,...
Question # 03 Mr. Hatim hold a diversified portfolio consisting of Pakistan State Oil, OGDC, Mobilink, Fauji Fertilizer Company, Zeal Pak Cement and KAPCO. He made an investment of Rs. 10,000 in each common stock. Beta of the portfolio is 1.17. After analyzing the market trends he decided to sell Zeal Pak Cement with a beta of 1.0 for Rs.10,000 and use the proceeds to buy Pakistan Tobacco Company with a beta of 1.65. On the basis of provided information...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT